One can put a material that readily emits photoelectrons on a negatively charged electroscope. The leaves of the electroscope will gradually drop as electrons are liberated from it by natural light. A similarly charged control electroscope should be placed nearby to show that the observed discharge is not due to leakage. Be warned thought that electrostatic experiments are tricky! One needs experience in order to get them under control. You could quantify the investigation by looking at different materials - the rate at which the leaves drop for different materials. Inserting different types of colour filters will display the colour dependence of the effect.

without equipment made specifically for the photoelectric effect, it could be tough to put together an experiment, but there might be an easy way, I cant say for sure. There are absolutley no easy ways whatsoever to test relativity. I would suggets going with the paper mache volcano.